{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3QUMDHHM4ESUOMUS4N3UEZFC7M","short_pith_number":"pith:3QUMDHHM","schema_version":"1.0","canonical_sha256":"dc28c19cece125473292e3774264a2fb11d077070857b0e52b928c1102199596","source":{"kind":"arxiv","id":"1607.07416","version":1},"attestation_state":"computed","paper":{"title":"Three New Results on Continuation Criteria for the 3D Relativistic Vlasov-Maxwell System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Neel Patel","submitted_at":"2016-07-25T19:14:28Z","abstract_excerpt":"In this paper, we consider sufficient conditions, called continuation criteria, for global existence and uniqueness of classical solutions to the three-dimensional relativistic Vlasov-Maxwell system. In the compact momentum support setting, we prove that $\\|p_{0}^{\\frac{18}{5r} - 1+\\beta}f\\|_{L^{\\infty}_{t}L^{r}_{x}L^{1}_{p}} \\lesssim 1$, where $1\\leq r \\leq 2$ and $\\beta >0$ is arbitrarily small, is a continuation criteria. The previously best known continuation criteria in the compact setting is $\\|p_{0}^{\\frac{4}{r} - 1+\\beta}f\\|_{L^{\\infty}_{t}L^{r}_{x}L^{1}_{p}} \\lesssim 1$, where $1\\leq "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.07416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-25T19:14:28Z","cross_cats_sorted":[],"title_canon_sha256":"92f5d6083d476cd5005868fb792c08e224d12ea6f573e210612f2f44bfbd4535","abstract_canon_sha256":"4720f14df0b097c258062659f6d4bbb2931fe02eccbba6c4b566100bf901a519"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:33.970535Z","signature_b64":"Q5AlMRy9CC+wqXvP1wCrz6KMgIU7+iU5CKEeeBQfoeoI4d5PWLVOMV2y7wRsBRlVASnZhOs1THW8PDph3YjrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc28c19cece125473292e3774264a2fb11d077070857b0e52b928c1102199596","last_reissued_at":"2026-05-18T01:10:33.970103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:33.970103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three New Results on Continuation Criteria for the 3D Relativistic Vlasov-Maxwell System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Neel Patel","submitted_at":"2016-07-25T19:14:28Z","abstract_excerpt":"In this paper, we consider sufficient conditions, called continuation criteria, for global existence and uniqueness of classical solutions to the three-dimensional relativistic Vlasov-Maxwell system. In the compact momentum support setting, we prove that $\\|p_{0}^{\\frac{18}{5r} - 1+\\beta}f\\|_{L^{\\infty}_{t}L^{r}_{x}L^{1}_{p}} \\lesssim 1$, where $1\\leq r \\leq 2$ and $\\beta >0$ is arbitrarily small, is a continuation criteria. The previously best known continuation criteria in the compact setting is $\\|p_{0}^{\\frac{4}{r} - 1+\\beta}f\\|_{L^{\\infty}_{t}L^{r}_{x}L^{1}_{p}} \\lesssim 1$, where $1\\leq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07416","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.07416","created_at":"2026-05-18T01:10:33.970174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.07416v1","created_at":"2026-05-18T01:10:33.970174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07416","created_at":"2026-05-18T01:10:33.970174+00:00"},{"alias_kind":"pith_short_12","alias_value":"3QUMDHHM4ESU","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3QUMDHHM4ESUOMUS","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3QUMDHHM","created_at":"2026-05-18T12:29:55.572404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M","json":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M.json","graph_json":"https://pith.science/api/pith-number/3QUMDHHM4ESUOMUS4N3UEZFC7M/graph.json","events_json":"https://pith.science/api/pith-number/3QUMDHHM4ESUOMUS4N3UEZFC7M/events.json","paper":"https://pith.science/paper/3QUMDHHM"},"agent_actions":{"view_html":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M","download_json":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M.json","view_paper":"https://pith.science/paper/3QUMDHHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.07416&json=true","fetch_graph":"https://pith.science/api/pith-number/3QUMDHHM4ESUOMUS4N3UEZFC7M/graph.json","fetch_events":"https://pith.science/api/pith-number/3QUMDHHM4ESUOMUS4N3UEZFC7M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M/action/storage_attestation","attest_author":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M/action/author_attestation","sign_citation":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M/action/citation_signature","submit_replication":"https://pith.science/pith/3QUMDHHM4ESUOMUS4N3UEZFC7M/action/replication_record"}},"created_at":"2026-05-18T01:10:33.970174+00:00","updated_at":"2026-05-18T01:10:33.970174+00:00"}